CN107703966A - A kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight - Google Patents

A kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight Download PDF

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CN107703966A
CN107703966A CN201710961249.2A CN201710961249A CN107703966A CN 107703966 A CN107703966 A CN 107703966A CN 201710961249 A CN201710961249 A CN 201710961249A CN 107703966 A CN107703966 A CN 107703966A
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CN107703966B (en
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段海滨
邱华鑫
魏晨
邓亦敏
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Beihang University
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    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
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Abstract

The present invention is a kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight, and implementation step is：Step 1：Initialization；Step 2：Determine leader；Step 3：Determine the vectoring aircraft of each wing plane；Step 4：Determine the desired locations of relatively each wing plane of vectoring aircraft；Step 5：Anticollision；Step 6：Generate the instruction of unmanned plane autopilot control input；Step 7：By autopilot control input instruction input unmanned plane model；Step 8：Judge whether to terminate emulation；This method aims to provide a kind of distributed unmanned plane autonomous formation control method, while unmanned plane group of planes robustness and adaptability is improved, reduces the calculating of unmanned plane unit and traffic load, so as to effectively improve unmanned plane capacity of will level.

Description

A kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight
Technical field
The present invention relates to a kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight, belong to unmanned plane control Field processed.
Background technology
Unmanned plane (Unmanned Aerial Vehicle, UAV) is one kind by itself programme-control or by wireless remotecontrol , for performing the unmanned vehicle of particular task, the attribute and environment with " platform nobody, system someone " adapt to energy Power is strong, autonomy is high, non-contact, zero injures and deaths, the characteristics of can working long hours, have in military and civilian field wide Application development prospect.
Limited because single unmanned plane exists in sensing range, task load-carrying, computing capability etc., it is some multiple performing Efficiency is low during miscellaneous task or can not complete.Compared with single unmanned plane, unmanned plane autonomous formation can low cost, the group of high dispersive The form of knitting meets functional requirement, so that decentralization MANET lifting system efficient information is shared, fault-resistant and self-healing ability, with work( Energy distribution improves system survival rate and efficiency exchanges ratio, it has also become the important trend of Development of UAV.Unmanned plane autonomous formation, The unmanned plane that referring to multi rack has capacity of will carries out three-dimensional arrangement according to certain structure type, and can in flight course Stable formation is kept, and formation dynamic can be carried out according to external circumstances and mission requirements and adjusted, to embody the coordination of a whole group of planes Uniformity.Although the flight of unmanned plane autonomous formation can improve systematic function, it is new that multiple aircraft and depositing also result in some Problem, such as the difficulty lifting of system coordination management, the uncertain increase of system integrality, dependence of the system to communication Increase, therefore efficient unmanned plane autonomous formation control method reasonable in design is most important.It is it is contemplated that a kind of by designing Unmanned plane autonomous formation control method, unmanned plane autonomous formation controlled level is improved, makes it efficient with relatively low load configuration Relative complex task is completed, so as to possess the capacity of will of certain intelligent grade.
At present, common unmanned plane autonomous formation control method mainly includes leader-wing plane formula, Behavior-based control, virtual knot Structure etc..Wherein leader-wing plane formula is, it is necessary to default formation structure, the poor robustness in terms of group of planes failure；Behavior-based control method is basis Presupposed information and trigger condition form control instruction, lack adaptability；Virtual architecture method is similar to a kind of centerized fusion, to calculating Ability dependence is strong, high communicating requirement machine.The present invention is for existing unmanned plane autonomous formation control method in robustness, suitable The problem of capacity of will deficiency of answering property etc. and calculating and excessive traffic load, based on wild goose group's self-organizing Flight Design A kind of distributed unmanned plane autonomous formation control method.
The linear formation flight of wild goose group is a kind of universal phenomenon present in nature, is that gregariousness individual is to adapt to existence ring Border, after inherent existence ability after long-term evolution.Wild goose group finally causes whole colony from macroscopically by individual decision making Emerge self-organization, collaborative, stability and the adaptability to environment；The purpose of unmanned plane autonomous formation is then to pass through distribution Formula decision-making is realized can self-organizing, harmony be good and the formation flight of strong robustness.In view of decentralization in Flight of geese mechanism Neighbouring individual interaction, overall self-organization the features such as locality, distribution and robust with the control of unmanned plane autonomous formation Property etc. requirement have closely agree with part, the present invention propose it is a kind of based on wild goose group self-organizing flight unmanned plane autonomous formation Control method, to solve deficiency of the existing unmanned plane autonomous formation control method on capacity of will and unit load, effectively Improve unmanned plane autonomous formation controlled level.
The content of the invention
1st, goal of the invention：
The invention provides a kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight, the purpose is to carry For a kind of distributed unmanned plane autonomous formation control method, it is intended to while improving unmanned plane group of planes robustness and adaptability, The calculating of unmanned plane unit and traffic load are reduced, so as to effectively improve unmanned plane capacity of will level.
2nd, technical scheme：
The present invention is directed to unmanned plane formation control problem, and it is autonomous to develop a kind of unmanned plane based on wild goose group self-organizing flight Formation control method, the implementation process of this method is as shown in figure 1, specific implementation step is as follows：
Step 1：Initialization
The initial flight state of random generation n frame unmanned planes, including locus (Xi,Yi,hi), horizontal velocity Vi, course Angle ψiAnd altitude rate ζi, wherein i is the numbering of unmanned plane；Set current simulation time t=0.
Step 2：Determine leader
The group of planes that n framves unmanned plane forms is considered as a wild goose group, wherein every frame unmanned plane is the individual in wild goose group, flown The leader that row state is not influenceed by other unmanned planes is the wild goose that leads the flock flying in formation in wild goose group.Current spatial location is located at of wild goose group forefront Body, it is considered as the wild goose that leads the flock flying in formation of the wild goose group；When multiple individuals be present and be located at wild goose group forefront, these individual spatial locations are located at wild goose group Leftmost individual, it is considered as the wild goose that leads the flock flying in formation of the wild goose group.I.e. and if only if meets X in the absence of unmanned plane jj≥XiAnd Yj≥YiWhen, have NumL=i, wherein NumLNumbered for unmanned plane corresponding to leader, X is transverse axis coordinate of the unmanned plane under earth axes, and Y is nothing The man-machine ordinate of orthogonal axes under earth axes, i are the numbering of unmanned plane
Step 3：Determine the vectoring aircraft of each wing plane
Wing plane is considered as from wild goose, and vectoring aircraft corresponding to wing plane is considered as preceding wild goose, wherein remaining in addition to leader in a group of planes Unmanned plane is wing plane, and the unmanned plane for influenceing a certain wing plane state of flight is the vectoring aircraft of the wing plane, and vectoring aircraft can be leader, It can be wing plane.Each it is currently located at from wild goose selection on front and horizontal plane at a distance of nearest individual as preceding wild goose；If front is without individual During body, from wild goose selection currently with itself individual side by side, in the horizontal plane at a distance of nearest individual as preceding wild goose；If it may be selected Preceding wild goose it is not unique when, select the minimum individual of numbering as preceding wild goose from wild goose.I.e. and if only if meets X in the absence of unmanned plane j'j' ≥XiAnd Rij'＜ RijWhen or meet Xj'≥Xi, Rij'=RijAnd during j'＜ j, haveWhereinFor the horizontal range between wing plane i and unmanned plane j,For the volume of vectoring aircraft corresponding to wing plane i Number.
Step 4：Determine the desired locations of relatively each wing plane of vectoring aircraft
When a certain current spatial location from wild goose is located on the right side of wild goose that leads the flock flying in formation, should can select to fly to the right side of wild goose before it is corresponded to from wild goose Side desired locations, on the contrary it should can select to fly to the left side desired locations of wild goose before it is corresponded to from wild goose.Preceding wild goose is relative to corresponding from wild goose Desired locations are desired locations of the vectoring aircraft relative to wing plane.Work asWhen, haveWhenWhen, have
WhereinWithRespectively vectoring aircraftForward direction desired locations and lateral desired locations relative to wing plane i, xexp And yexpIt is respectively preceding to desired distance and lateral desired distance.
Step 5：Anticollision
When the current location of wantonly two framves unmanned plane is unsatisfactory for safety condition, to prevent from colliding, underlying unmanned plane One section of distance to a declared goal will be declined.Work as | x |≤xmin, | y |≤ymin, | z |≤zminAnd during z ＜ 0, if i=NumL, then haveIf i ≠ NumL,
Then haveIf otherwise i=NumL, then haveIf i ≠ NumL, then have zi=0.Wherein, (x, y, Z) it is position of certain frame unmanned plane under unmanned plane i rotating coordinate systems, the origin O of the rotating coordinate system is located in unmanned plane i The heart, x-axis and ViUnanimously, z-axis is vertically (downwards for just), and y-axis is perpendicular to Oxz planes (for just on the right side of body)；For length Machine highly keeps the control input of autopilot, hcFor anticollision command range,For vectoring aircraftRelative to the wing plane i vertical phase Hope position, xmin、yminAnd zminRespectively forward secrecy distance, laterally security distance and vertical safe distance, h fly for unmanned plane Row height.
Step 6：Generate the instruction of unmanned plane autopilot control input
Leader speed keeps autopilot control inputAutopilot control input is kept with courseA respectively upper sampling The corresponding states at moment, i.e.,The speed of wing plane keeps autopilot control input VWc, course keep from Drive instrument control input ψWcAnd height keeps autopilot control input hWcIt can be described as：
WhereinWithIt is the pid control parameter of x, y and z passage respectively,For the error of x passages,For the error of y passages,For the error of z passages, kx、kV、ky、kψAnd kzRespectively forward error, velocity error, lateral error, course are missed The control gain of difference and height error.
Step 7：By autopilot control input instruction input unmanned plane model
, will if unmanned plane i is leaderWithThe leader model described by following formula is inputted, when obtaining next emulation Between unmanned plane state：
Wherein τV、τψ(τa,τb) it is respectively that speed keeps autopilot, course to keep autopilot and height to keep self-driving The time constant of instrument.
, will if unmanned plane i is wing planeWithThe wing plane model described by following formula is inputted, when obtaining next emulation Between unmanned plane state：
WhereinIt is unmanned planeHeight keep autopilot control input,It is average dynamic pressure, S is wing area, m It is gross weight,AndIt is the stability derivative of resistance, side force and lift variation respectively.
Step 8：Judge whether to terminate emulation
Simulation time t=t+ts, wherein ts are the sampling time.If t is more than maximum simulation run time Tmax, then knot is emulated Beam simultaneously draws unmanned plane group of planes flight path and condition curve；Otherwise, return to step two.
3rd, advantage and effect：
The present invention proposes a kind of unmanned plane autonomous formation control method based on wild goose group self-organizing flight.The master of this method Advantage is wanted to be mainly reflected in two aspects：On the one hand, this method is to imitate the neighbouring individual interaction of decentralization in Flight of geese A kind of distributed unmanned plane autonomous formation control method of Mechanism Design, therefore compared to centralizations such as common virtual architectures Unmanned plane autonomous formation control method, it this method reduce unit calculating and traffic load；On the other hand, this method has adhered to wild goose Self-organization in group's fly mechanics, with common leader-wing plane formula, Behavior-based control method etc. rely on the unmanned plane of presupposed information from Main formation control method, there is higher robustness and adaptability, and then effectively increase unmanned plane capacity of will level.
Brief description of the drawings
The unmanned plane autonomous formation control flow that Fig. 1 is flown based on wild goose group self-organizing.
Fig. 2 unmanned plane group of planes flight paths.
Fig. 3 unmanned plane group of planes altitude curves.
Fig. 4 unmanned plane group of planes horizontal velocity curves.
Fig. 5 unmanned plane group of planes course angular curve.
Fig. 6 unmanned plane group of planes altitude rate curves.
Label and symbol description are as follows in figure：
T --- simulation time
I --- unmanned plane is numbered
N --- unmanned plane quantity
Tmax--- the maximum simulation run time
Ts --- the sampling time
N --- it is unsatisfactory for condition (no)
Y --- meet condition (YES)
H --- unmanned plane height
V --- unmanned plane speed
ψ --- unmanned plane course angle
ζ --- unmanned plane altitude rate
Embodiment
See Fig. 1 to Fig. 6, control example proposed by the invention to verify below by a specific unmanned plane autonomous formation Method validity.Experimental calculation machine is configured to Intel Core i7-6700HQ processors, 2.60Ghz dominant frequency, in 16G Deposit, software is MATLAB 2014a versions.This method comprises the following steps that：
Step 1：Initialization
The initial flight state of 12 frame unmanned planes of random generation：The initial spatial location of unmanned plane 1 to unmanned plane 12 is distinguished For (4.3200m, 4.0930m, 112.9507m), (8.2271m, 8.6110m, 117.4897m), (12.4510m, 12.7517m, 104.2471m)、(16.1673m,16.4915m,102.8107m)、(20.2292m,20.4849m,133.3898m)、 (23.8720m,23.6837m,121.6000m)、(28.1967m,27.7187m,132.6017m)、(32.1072m, 31.8181m, 120.0093m), (35.4427m, 36.2482m, 103.7010m), (40.1160m, 39.3100m, 130.6508m), (43.6097m, 44.0691m, 116.8043m) and (47.2467m, 47.6949m, 132.6842m), just Beginning horizontal velocity is 42m/s, and initial heading angle is 0 °, and elemental height rate of change is 0m/s2；Set current simulation time T=0s.
Step 2：Determine leader
The group of planes that 12 frame unmanned planes form is considered as a wild goose group, wherein every frame unmanned plane is the individual in wild goose group, Leader is the wild goose that leads the flock flying in formation in wild goose group.Locus is located at No. 12 individuals of wild goose group forefront, is considered as the wild goose that leads the flock flying in formation of the wild goose group.That is leader pair The unmanned plane numbering Num answeredL=12.
Step 3：Determine the vectoring aircraft of each wing plane
Wing plane is considered as from wild goose, and vectoring aircraft corresponding to wing plane is considered as preceding wild goose.Each front and water are currently located at from wild goose selection At a distance of nearest individual as preceding wild goose in plane；If front is without individual, from wild goose selection currently with itself individual side by side, in level At a distance of nearest individual as preceding wild goose on face；If selectable preceding wild goose is not unique, the minimum individual of numbering is selected as preceding wild goose from wild goose. In example, No. 2~No. 12 individuals are No. 1~No. 11 individual preceding wild geese respectively.Vectoring aircraft is numbered i.e. corresponding to wing plane iRespectively：
Step 4：Determine the desired locations of relatively each wing plane of vectoring aircraft
When a certain current spatial location from wild goose is located on the right side of wild goose that leads the flock flying in formation, should can select to fly to the right side of wild goose before it is corresponded to from wild goose Side desired locations, on the contrary it should can select to fly to the left side desired locations of wild goose before it is corresponded to from wild goose.Preceding wild goose is relative to corresponding from wild goose Desired locations are desired locations of the vectoring aircraft relative to wing plane.In example, forward direction desired distance xexp=3.9200m, lateral phase Hope distance yexp=1.5394m, the forward direction desired locations of relatively each wing plane of vectoring aircraftIt is 3.9200m, longitudinal desired locations It is -1.5394m.
Step 5：Anticollision
When the current location of wantonly two framves unmanned plane is unsatisfactory for safety condition, to prevent from colliding, underlying unmanned plane One section of distance to a declared goal will be declined.In example, forward secrecy distance xmin, laterally security distance yminAnd vertical safe distance zmin Respectively 2.7500m, 2.1560m and 0.8956m, anticollision command range hc=1.6284m.When exist certain frame unmanned plane in nothing Position (x, y, z) under man-machine i rotating coordinate systems meets | x |≤xmin, | y |≤ymin, | z |≤zminAnd during z ＜ 0, if i=12, Then leader highly keeps the control input of autopilotIf i ≠ 12, vectoring aircraftRelative to the vertical of wing plane i Desired locationsIf otherwise i=12,If i ≠ 12,
Step 6：Generate the instruction of unmanned plane autopilot control input
Leader speed keeps autopilot control inputAutopilot control input is kept with courseA respectively upper sampling The corresponding states at moment, i.e.,The speed that wing plane is obtained by formula (1) keeps autopilot control input VWc, boat To holding autopilot control input ψWcAnd height keeps autopilot control input hWc, the wherein pid control parameter of x passages
The pid control parameter of y passages
The pid control parameter of z passages
Forward error control gain kx=-10, velocity error control gain kV=3, lateral error control gain ky=- 0.1, course error control gain kψ=1, height error control gain kz=10.
Step 7：By autopilot control input instruction input unmanned plane model
, will if unmanned plane i is leaderWithLeader model described by input type (2), when obtaining next emulation Between unmanned plane state, its medium velocity keep autopilot timeconstantτV=5s, course keep autopilot timeconstantτψ= 0.75s, height keep autopilot time constant (τa,τb)=(0.3075,3.85)., will if unmanned plane i is wing plane WithWing plane model described by input type (3), the unmanned plane state of next simulation time is obtained, whereinIt is unmanned plane Height keep the control input of autopilot, average dynamic pressureWing area S=1.37m2, gross weight m=20.64kg, The stability derivative of resistance changeThe stability derivative of side force changeRise The stability derivative of power change
Step 8：Judge whether to terminate emulation
Simulation time t=t+0.01s.If t is more than 6s, emulation terminates and draws unmanned plane group of planes flight path and state Curve；Otherwise, return to step two.Overall process unmanned plane during flying track, altitude curve, horizontal velocity curve, course angular curve with And altitude rate curve difference is as shown in Figures 2 to 6.Unmanned plane simulating, verifying is by proposed by the invention based on wild goose group The unmanned plane autonomous formation control method of self-organizing flight, a unmanned plane group of planes can realize autonomous formation.

Claims (1)

  1. A kind of 1. unmanned plane autonomous formation control method based on wild goose group self-organizing flight, it is characterised in that：This method is specifically real Existing step is as follows：
    Step 1：Initialization
    The initial flight state of random generation n frame unmanned planes, including locus (Xi,Yi,hi), horizontal velocity Vi, course angle ψi And altitude rate ζi, wherein i is the numbering of unmanned plane；Set current simulation time t=0；
    Step 2：Determine leader
    The group of planes that n framves unmanned plane forms is considered as a wild goose group, wherein every frame unmanned plane is the individual in wild goose group, flight shape The leader that state is not influenceed by other unmanned planes is the wild goose that leads the flock flying in formation in wild goose group；Current spatial location is located at the individual of wild goose group forefront, depending on For the wild goose that leads the flock flying in formation of the wild goose group；When multiple individuals be present and be located at wild goose group forefront, it is most left that these individual spatial locations are located at wild goose group The individual on side, it is considered as the wild goose that leads the flock flying in formation of the wild goose group；I.e. and if only if meets X in the absence of unmanned plane jj≥XiAnd Yj≥YiWhen, there is NumL= I, wherein NumLNumbered for unmanned plane corresponding to leader, X is transverse axis coordinate of the unmanned plane under earth axes, and Y is unmanned plane Ordinate of orthogonal axes under earth axes, i are the numbering of unmanned plane；
    Step 3：Determine the vectoring aircraft of each wing plane
    Wing plane is considered as from wild goose, and vectoring aircraft corresponding to wing plane is considered as preceding wild goose, wherein remaining in addition to leader in a group of planes nobody Machine is wing plane, and the unmanned plane for influenceing a certain wing plane state of flight is the vectoring aircraft of the wing plane, and vectoring aircraft can be leader, or Wing plane；Each it is currently located at from wild goose selection on front and horizontal plane at a distance of nearest individual as preceding wild goose；If front is without individual, From wild goose selection currently with itself individual side by side, in the horizontal plane at a distance of nearest individual as preceding wild goose；If before selectable When wild goose is not unique, the minimum individual of numbering is selected as preceding wild goose from wild goose；I.e. and if only if meets X in the absence of unmanned plane j'j'≥Xi And Rij' ＜ RijWhen or meet Xj'≥Xi, Rij'=RijAnd during j'＜ j, haveWherein For the horizontal range between wing plane i and unmanned plane j,For the numbering of vectoring aircraft corresponding to wing plane i；
    Step 4：Determine the desired locations of relatively each wing plane of vectoring aircraft
    When a certain current spatial location from wild goose is located on the right side of wild goose that leads the flock flying in formation, should can select to fly to the right side phase of wild goose before it is corresponded to from wild goose Position is hoped, otherwise should can select to fly to the left side desired locations of wild goose before it is corresponded to from wild goose；Preceding wild goose is relative to the corresponding expectation from wild goose Position is desired locations of the vectoring aircraft relative to wing plane；Work asWhen, haveWhenWhen, HaveWhereinWithRespectively vectoring aircraftForward direction desired locations and lateral expectation relative to wing plane i Position, xexpAnd yexpIt is respectively preceding to desired distance and lateral desired distance；
    Step 5：Anticollision
    When the current location of wantonly two framves unmanned plane is unsatisfactory for safety condition, to prevent from colliding, underlying unmanned plane is by under One section of distance to a declared goal drops；Work as | x |≤xmin, | y |≤ymin, | z |≤zminAnd during z ＜ 0, if i=NumL, then have If i ≠ NumL, then haveIf otherwise i=NumL, then haveIf i ≠ NumL, then haveWherein, (x, Y, z) it is position of certain frame unmanned plane under unmanned plane i rotating coordinate systems, the origin O of the rotating coordinate system is located at unmanned plane i's Center, x-axis and ViUnanimously, vertically, y-axis is perpendicular to Oxz planes for z-axis；The control of autopilot is highly kept for leader Input, hcFor anticollision command range,For vectoring aircraftRelative to wing plane i vertical desired locations, xmin、yminAnd zminRespectively For forward secrecy distance, laterally security distance and vertical safe distance, h is unmanned plane during flying height；
    Step 6：Generate the instruction of unmanned plane autopilot control input
    Leader speed keeps autopilot control inputAutopilot control input is kept with courseA respectively upper sampling instant Corresponding states, i.e.,The speed of wing plane keeps autopilot control input VWc, course keep autopilot Control input ψWcAnd height keeps autopilot control input hWcIt can be described as：
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    WhereinWithIt is the pid control parameter of x, y and z passage respectively,For the error of x passages,For the error of y passages,For the error of z passages, kx、kV、ky、kψAnd kzRespectively forward error, velocity error, lateral error, course are missed The control gain of difference and height error；
    Step 7：By autopilot control input instruction input unmanned plane model
    , will if unmanned plane i is leaderWithThe leader model described by following formula is inputted, obtains next simulation time Unmanned plane state：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mover> <mi>X</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <msup> <mi>V</mi> <mi>i</mi> </msup> <msup> <mi>cos&amp;psi;</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>Y</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <msup> <mi>V</mi> <mi>i</mi> </msup> <msup> <mi>sin&amp;psi;</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>h</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <msup> <mi>&amp;zeta;</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>V</mi> </msub> </mfrac> <msup> <mi>V</mi> <mi>i</mi> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>V</mi> </msub> </mfrac> <msub> <mi>V</mi> <msub> <mi>L</mi> <mi>C</mi> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>&amp;psi;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msup> <mi>&amp;psi;</mi> <mi>i</mi> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msub> <mi>&amp;psi;</mi> <msub> <mi>L</mi> <mi>C</mi> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>&amp;zeta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mfrac> <mo>)</mo> </mrow> <msup> <mi>&amp;zeta;</mi> <mi>i</mi> </msup> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mrow> </mfrac> <msup> <mi>h</mi> <mi>i</mi> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mrow> </mfrac> <msub> <mi>h</mi> <msub> <mi>L</mi> <mi>C</mi> </msub> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein τV、τψ(τa,τb) be respectively speed keep autopilot, course keep autopilot and height keep autopilot when Between constant；
    , will if unmanned plane i is wing planeWithThe wing plane model described by following formula is inputted, obtains next simulation time Unmanned plane state：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mfrac> <msup> <mover> <mi>y</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msup> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msup> <mi>&amp;psi;</mi> <mi>i</mi> </msup> <mo>-</mo> <msup> <mi>V</mi> <mi>i</mi> </msup> <mo>+</mo> <msub> <mi>V</mi> <msubsup> <mi>N</mi> <mrow> <mi>l</mi> <mi>e</mi> <mi>a</mi> <mi>d</mi> </mrow> <mi>i</mi> </msubsup> </msub> <mo>+</mo> <mfrac> <msup> <mover> <mi>y</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msup> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msub> <mi>&amp;psi;</mi> <msub> <mi>W</mi> <mi>C</mi> </msub> </msub> <mo>+</mo> <msup> <mover> <mi>y</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msup> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> </mrow> <mrow> <msup> <mi>mV</mi> <mi>i</mi> </msup> </mrow> </mfrac> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>Y</mi> <msub> <mi>W</mi> <mi>y</mi> </msub> </msub> </msub> <mi>y</mi> <mo>+</mo> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>Y</mi> <msub> <mi>W</mi> <mi>z</mi> </msub> </msub> </msub> <mi>z</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>y</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <mo>-</mo> <msup> <mi>V</mi> <mi>i</mi> </msup> <mo>)</mo> </mrow> <msup> <mi>&amp;psi;</mi> <mi>i</mi> </msup> <mo>+</mo> <msup> <mi>V</mi> <mi>i</mi> </msup> <msup> <mi>&amp;psi;</mi> <mi>i</mi> </msup> <mo>-</mo> <mfrac> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msup> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msub> <mi>&amp;psi;</mi> <msub> <mi>W</mi> <mi>C</mi> </msub> </msub> <mo>-</mo> <msup> <mover> <mi>x</mi> <mo>&amp;OverBar;</mo> </mover> <mi>i</mi> </msup> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> </mrow> <mrow> <msup> <mi>mV</mi> <mi>i</mi> </msup> </mrow> </mfrac> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>Y</mi> <msub> <mi>W</mi> <mi>y</mi> </msub> </msub> </msub> <mi>y</mi> <mo>+</mo> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>Y</mi> <msub> <mi>W</mi> <mi>z</mi> </msub> </msub> </msub> <mi>z</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <msup> <mi>&amp;zeta;</mi> <mi>i</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>V</mi> </msub> </mfrac> <msup> <mi>V</mi> <mi>i</mi> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>V</mi> </msub> </mfrac> <msub> <mi>V</mi> <msub> <mi>W</mi> <mi>C</mi> </msub> </msub> <mo>+</mo> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> </mrow> <mi>m</mi> </mfrac> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>D</mi> <msub> <mi>W</mi> <mi>y</mi> </msub> </msub> </msub> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>&amp;psi;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msup> <mi>&amp;psi;</mi> <mi>i</mi> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>&amp;psi;</mi> </msub> </mfrac> <msub> <mi>&amp;psi;</mi> <msub> <mi>W</mi> <mi>C</mi> </msub> </msub> <mo>+</mo> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> </mrow> <mrow> <msub> <mi>mV</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>Y</mi> <msub> <mi>W</mi> <mi>y</mi> </msub> </msub> </msub> <mi>y</mi> <mo>+</mo> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>Y</mi> <msub> <mi>W</mi> <mi>z</mi> </msub> </msub> </msub> <mi>z</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>&amp;zeta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msup> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mfrac> <mo>)</mo> </mrow> <msup> <mi>&amp;zeta;</mi> <mi>i</mi> </msup> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mrow> </mfrac> <mi>z</mi> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mrow> </mfrac> <msub> <mi>h</mi> <msub> <mi>W</mi> <mi>C</mi> </msub> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;tau;</mi> <mi>a</mi> </msub> <msub> <mi>&amp;tau;</mi> <mi>b</mi> </msub> </mrow> </mfrac> <msub> <mi>h</mi> <mrow> <msub> <msup> <mi>L</mi> <mo>&amp;prime;</mo> </msup> <mi>C</mi> </msub> </mrow> </msub> <mo>+</mo> <mfrac> <mrow> <mover> <mi>q</mi> <mo>&amp;OverBar;</mo> </mover> <mi>S</mi> </mrow> <mi>m</mi> </mfrac> <msub> <mi>&amp;Delta;C</mi> <msub> <mi>L</mi> <msub> <mi>W</mi> <mi>y</mi> </msub> </msub> </msub> <mi>y</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    WhereinIt is unmanned planeHeight keep autopilot control input,It is average dynamic pressure, S is wing area, and m is hair Weight,AndIt is the stability derivative of resistance, side force and lift variation respectively；
    Step 8：Judge whether to terminate emulation
    Simulation time t=t+ts, wherein ts are the sampling time；If t is more than maximum simulation run time Tmax, then emulate and terminate simultaneously Draw unmanned plane group of planes flight path and condition curve；Otherwise, return to step two.
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